 Hello and welcome to the session. I am Deepika and I am going to help you to solve the following question. The question says if y is equal to sin of log x prove that x square into d square y over dx square plus x into dy by dx plus y is equal to 0. So let's start the solution. Now we have y is equal to sin of log x therefore dy by dx is equal to cos of log x into derivative of log x which is 1 over x or x into dy by dx is equal to cos of log x. Now on differentiating again both sides of above equation with respect to x we get into d2y over dx square plus dy by dx into 1 is equal to minus sin of log x into 1 over x or x square into d2y over dx square. Plus x dy by dx plus sin of log x is equal to 0 or this can be written as x square into d2y over dx square plus x dy by dx. Plus now y is equal to sin of log x so we have x square into d2y over dx square plus x dy by dx plus y is equal to 0. Hence we have proved that if y is equal to sin of log x then x square into d2y over dx square plus x dy by dx plus y is equal to 0. So this completes our session. I hope the solution is clear to you. Bye and have a nice day.